On the Pricing of Interest Rate Derivatives with a Stochastic Basis; From FRA’s to Bermudan Swaptions

Specialeforsvar ved Andreas Gylden

Titel: On the Pricing of Interest Rate Derivatives with a Stochastic BasisFrom FRA’s to Bermudan Swaptions

Abstract: Prior to the financial crisis of 2008, basis spreads of interbank deposit rates were considered practically negligible, stationary and independent of tenor fixing. During the crisis basis spreads widened and seemed to evolve stochastically. This fundamentally changed the theory for valuation of interest rate derivatives. This thesis presents general and model independent pricing formulas for interest rate derivatives in the multi-curve framework. It is showed that the simplicity of the pricing formulas depend on the definition of the basis spread.An introduction of the generic stochastic basis spread model of Mercurio and Xie (2012) which can be plugged on top of any of the classical term structure models is given. The model does not preclude the possibility of negative basis spreads. An analysis of this drawback concludes that the effect of the stochastic basis model is negligible when the model parameters are chosen such that the probability of negative basis spreads is zero. Semi-analytical pricing formulas for caplets and European swaptions are derived in the stochastic basis spread model of Mercurio and Xie (2012) on top of the one-factor Hull- White short rate model. An in depth analysis is presented for the stochastic basis spread effects for forward rate agreements, interest rate swaps, caps and European swaptions using the Hull-White model. In addition, the analysis is performed with the stochastic basis spread model on top of a 4-factor LIBOR Market Model. This leads to an analysis of the consistency between terminal swap rate distributions at the exercise dates of a Bermudan swaption when the Bermudan prices are generated by the 4-factor LIBOR Market Model and the Hull-White model. It is concluded that the stochastic basis spread model allows for Bermudan swaption prices in the Hull-White model being similar to those produced by the 4-factor LIBOR Market Model.